PLEASE HELP ASAP WITH THIS

Molar mass of Al = 26.98 g/mol

mass of Al = 33.0 g

we have below equation to be used:

number of mol of Al,

n = mass of Al/molar mass of Al

=(33.0 g)/(26.98 g/mol)

= 1.223 mol

Molar mass of Cl2 = 70.9 g/mol

mass of Cl2 = 38.0 g

we have below equation to be used:

number of mol of Cl2,

n = mass of Cl2/molar mass of Cl2

=(38.0 g)/(70.9 g/mol)

Part B

we have the Balanced chemical equation as:

2 Al + 3 Cl2 ---> 2 AlCl3

2 mol of Al reacts with 3 mol of Cl2

for 1.2231 mol of Al, 1.8347 mol of Cl2 is required

But we have 0.536 mol of Cl2

so, Cl2 is limiting reagent

we will use Cl2 in further calculation

Molar mass of AlCl3 = 1*MM(Al) + 3*MM(Cl)

= 1*26.98 + 3*35.45

= 133.33 g/mol

From balanced chemical reaction, we see that

when 3 mol of Cl2 reacts, 2 mol of AlCl3 is formed

mol of AlCl3 formed = (2/3)* moles of Cl2

= (2/3)*0.536

part 1: the half-life of the element is 22 years.

part 2: it will take 132.02 year for the sample to decay from 308.0 g to 4.8125 g.

explanation:

part 1: there are two ways to determine the half life time.

first way: the half life time can be determined directly from its definition as it is the time required for the sample to decay to its half concentration.

from the data the initial concentration was 45.0 g and decayed to its half value (22.5 g) in 22.0 years.

second way: the radio active decay is considered first order reaction so we can use the laws of first order reactions.

k = (1/t) ln (a/a-x), where k is the rate constant of the reaction,

t is the time of the reaction

a is the initial concentration of the reactant

a-x is the remaining concentration at time (t)

a = 45.0 g the initial concentration at t = 0 year.

at t = 22 year, a-x = 22.5 g

then k = (1/22 year) ln (45.0 g/ 22.5 g) = 0.0315 year-1.

the half-life time (t1/2) = ln 2/ k = 0.693/ k =0.693/ 0.0315 = 22 years.

part 2:

using the same law k = (1/t) ln (a/a-x),

using the given data; a = 308.0 g and a-x = 4.8125 g and the calculated k from the part 1 (k = 0.0315 year-1)

t = (1/k) ln (a/a-x) = (1/0.0315) ln (308.0/ 4.8125) = 132.02 years